GSEB Class 8 Maths Notes Chapter 11 Mensuration

   

This GSEB Class 8 Maths Notes Chapter 11 Mensuration covers all the important topics and concepts as mentioned in the chapter.

Mensuration Class 8 GSEB Notes

→ Perimeter: It is the distance around the boundary of any figure. Perimeter becomes the sum of all sides of the given figure. It is measured using units.

→ Perimeter of different figures:

  • Square = 4 × length Rectangle = 2 (length + breadth)
  • Triangle = sum of lengths of all 3 sides Perimeter of any regular polygon
    = Number of sides × Length of each side The perimeter of a circle is called its circumference.
  • Circumference = 2 πr [r = radius]
  • Perimeter of semicircle = \(\frac{2 \pi r}{2}\) = πr

→ Area: Area is the part of the plane occupied by a closed figure. A closed figure can be of different regular and irregular shapes. It is measured using square units.

→ Area of different figures :

  • Square = (side)2
  • Rectangle = length × breadth
  • Triangle = \(\frac{1}{2}\) × base × height
    = \(\frac{1}{2}\) × b × h
  • Parallelogram = base × height = b × h
  • Trapezium = \(\frac{1}{2}\) × (sum of parallel sides) × height
  • Rhombus = \(\frac{1}{2}\) × product of diagonals
    = \(\frac{1}{2}\) × d1 × d2
  • Circle = πr2 (r = radius)

→ Cuboid: It is a solid bounded by six rectangular plane regions.
GSEB Class 8 Maths Notes Chapter 11 Mensuration 1

  • Lateral surface area of a cubold
    = 2 × height × (length + breadth)
    = 2 × h × (l + b)
  • Total surface area of cubold
    = 2 (lb + bh + hl)

GSEB Class 8 Maths Notes Chapter 11 Mensuration

→ Cube: It is a special type of a cubold whose length, breadth and height are all equal.
GSEB Class 8 Maths Notes Chapter 11 Mensuration 2

  • Lateral surface area of a cube
    = 4 × (side)2 = 4l2
  • Total surface area of a cube
    = 6 × (side)2 = 6l2

→ Cylinder:

  • A pipe of water, a cistern to store grains. a tin of talcum powder. a 1-rupee coin, etc. are some objects having cylindrical shape.
  • A cylinder has two flat a top and a base. The the cylinder Is not flat as curved surface of the Cylinder circular surfaces. other surface of and It Is known cylinder.

GSEB Class 8 Maths Notes Chapter 11 Mensuration 3

  • The top and the base of a cylinder are circles of same size and hence their areas are equal.
  • Area of the base of a cylinder = r2. where r = radius of the base of the cylinder (also called radius of the cylinder)
  • Circumference of the base of a cylinder = 2r
    = πd. where d = diameter of the cylinder

→ Curved surface area of a cylinder
= circumference × height
= 2πr × h = 2πrh
OR
Curved surface area of a cylinder
= circumference × height
= πd × h = πdh

→ Volume: The measure of space occupied by a three dimensional object is called Its volume.

→ Volume of a cubold
= Area of the base × Height
= l × b × h

→ Volume of a cube: l × l × l = l3

→ Volume of a cylinder
GSEB Class 8 Maths Notes Chapter 11 Mensuration 4
= Area of the base × Height
= Area of the circle × Height
= πr2 × h = πr2h
Where r Is the radius of the base of the cylinder and h Is the height of the cylinder.

→ All the coins like 1-rupee coin. 2-rupee coin. 5-rupee coin and 10-rupee coin are cylindrical In shape.
GSEB Class 8 Maths Notes Chapter 11 Mensuration 5
Of course, taken only one coin, the height is quite less as compared to the radius. But, when more coins of the same type are stacked, they form a cylinder with considerable height.

GSEB Class 8 Maths Notes Chapter 11 Mensuration

→ The volume of liquids and gases that do not have fixed shape are usually measured In units like litres and millilitres (ml).

→ Remember:

  • 1 m3 = 10,00,000 cm3
  • 1 litre = 1000 millilitres
  • 1 m3 = 1000 litres
  • I litre = 1000 cm3
  • 1 m3 = 1000 litres
  • 1 cm3 = 1 millilitre

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